Chrono Trigger was the brainchild of several creative masterminds: Hironobu Sakaguchi, Yuji Horii, and Akira Toriyama, creators, respectively, of Final Fantasy, Dragon Quest and Dragon Ball. The fact that these men got together at a time when Final Fantasy and Dragon Quest were developed by different companies was the first clue something special was on the horizon.
By eschewing the tradition of random battles that whisked you away to a separate battle screen, Chrono Trigger quickly made it apparent that it was going to be a new experience. Right as the Final Fantasy series was implementing game systems that robbed characters of their uniqueness in battle, Chrono Trigger's battle system featured Techs, in which 2 or 3 characters could employ powerful abilities based on each party member's unique skill set. While the plot ended up boiling down to the 'prevent the apocalypse' variety, the scope of the game's events and the six different time periods visited set the title apart. Much like Homer Simpson's time-traveling escapades, events in the distant past could have major implications on the world (and its treasures) of the present and future.
There's more than a single reason the game grabbed people's attention: Whether it was the eclectic cast, unique gameplay, memorable musical score, or the simple desire to fly across time and space in your own time machine, it was (and is still) hard not to find something to love in Chrono Trigger.
Now, can we get that third game, Square Enix? It's about time.